> What they are saying is that you can't make a non-arbitrary identification of each dimension. You can call them 1,2,3, and I can call them 2,3,1, and that cha

> What they are saying is that you can't make a non-arbitrary identification of each dimension. You can call them 1,2,3, and I can call them 2,3,1, and that changes nothing except your arbitrary labels. I don't understand the point. What is the supposed consequence of that? As far as I can tell, it's an empty statement. And as I said, there are only two orientations in three dimensions. For an orientation, which is an equivalence class of ordered bases, the order actually does matter. You can call them whatever you want, but once you've called them something, their order matters, which was my original retort.